Question

Solve: 11x − 4 < 15x + 4 ≤ 13x + 14, x ∈ W and represent the solution set on a real number line.

Answer 1

Compound inequality:

11x − 4 < 15x + 4 ≤ 13x + 14

Break into two inequalities:

11x − 4 < 15x + 4 and

15x + 4 ≤ 13x + 14

First:

11x − 4 < 15x + 4 

⇒ −4 − 4 < 15x − 11x

⇒ −8 < 4x 

⇒ −2 < x

Second:

15x + 4 ≤ 13x + 14

⇒ 15x − 13x ≤ 14 − 4

⇒ 2x ≤ 10

⇒ x ≤ 5

Combine: −2 < x ≤ 5, so the real solution is the interval (−2, 5).

Since x ∈ W (the set of whole numbers W = {0, 1, 2, 3, ...}), the admissible whole-number are {0, 1, 2, 3, 4, 5}.